Titius’ Law

I first came across this law, believe it or not, in the fourth grade. We had an extremely primitive book on astronomy (by today’s standards, that is) on our class library shelf. Me and my two buddies that year basically divided all our free in-class time between that book, this comic book, and a chess set.

Anyway, that astronomy book first introduced me to Titius’ Law.* It’s amazing to me. I’ve come across it numerous times over the years in my readings, and it never ceases to make me shake my head in wonder. Perhaps when I have some free time I may dig deeper into its mystery. Officially, I believe, though, it’s regarded as nothing more than simple coincidence.

In 1770, a German mathematics professor named Johann Titius made an astonishing discovery. Fiddling about one night, he created a series by starting with 0, adding a 3, then doubling each number. This gives 0, 3, 6, 12, 24, 48, 96, 192 for the first eight terms. He then added 4 to each number and divided by 10. This changes those eight terms to

0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, and 19.6.

Okay. Now, in astronomy there is a unit of distance called the Astronomical Unit, or AU. This is simply the average distance between the Earth and the Sun. 1 AU is the distance between our planet and our sun. Typically, this distance is about 93 million miles, so 1 AU equals 93 million miles.

Neptune wasn’t discovered until 1845; nor was Pluto until 1930. If you take each of the seven known planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, and Uranus **) and find their average orbital distances in AUs, you get this series:

0.4, 0.7, 1.0, 1.5, 5.2, 9.5, and 19.2.

Titius noticed two things immediately. First, the numbers from his artificially generated series and the series describing the planets’ orbits in AUs sync up eerily well. So well, in fact, that it lent serious weight to his second observation: why is there no planet lying in orbit around 2.8 AUs?

At the climax of the 18th century this question had the astronomical world on fire. On January 1, 1801, astronomer Giuseppe Piazzi spotted a faint, tiny object orbiting about that mysterious distance. It was named Ceres, about 600 miles in diameter, and was the first asteroid to be discovered. Today we’ve found over 20,000 such asteroids, or minor planets as their now known, with up to 20, 30, or 50 new ones discovered every year, though only 15 have diameters over 150 miles. Asteroids are officially designated with a number (showing the order of discovery) and a name. So the first four asteroids are 1 Ceres, 2 Pallas, 3 Juno, and 4 Vesta.

An early hypothesis, prompted and supported by Titius’ “Law”, speculated that these asteroids were part of a planet that exploded or perhaps never completely formed. However, later analysis revealed that all the mass of all the known and suspected numbers of asteroids wouldn’t even add up to a tenth of the Moon’s mass. So, they are not the remnants of a planet or a protoplanet. Most likely they’re solar system debris herded into slightly spread out orbits between Mars and Jupiter by the tremendous gravitational power of the great gas giant.

Still, though, kinda interesting they reside where Titius series predicted they would.


* This is also known as the Titius-Bode law. Bode was a younger contemporary of Titius; their exact working relationship is not known to me offhand.

** Technically, Uranus was not discovered until 10 years or so after Titius formulated this law.